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If an animal was mostly slaughtered by a Jew (the majority but not all of the trachea & esophagus were cut) and the animal is not dying, a non-Jew can kill it however he wants and the animal will be kosher. If a Jew shechted the rest of the way, it would be a shihiyah b'miut batra (a pause in the final portion) and the animal is neveila (not kosher). But since the slaughter of a non-Jew is nothing, the majority slaughtered by the Jew is all that counts.

If a Jew did so for some reason (e.g. he had a blood-sugar emergency), we would trust him, just as an Ashkenazi can trust a Sefardi who trusts a non-Jew, or we can taste a fleishig-sliced onion for meatiness.
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ShalomOct 5 '10 at 23:03

2

Avoda Zara the non jew changes the status - by tasting food the jew still is the one who determines whether the food is Kosher.
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Gershon GoldOct 6 '10 at 2:30